Multivariate_linear_regression.ipynb

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    "# Multivariate linear regression"
   ]
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   "source": [
    "import numpy as np"
   ]
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    "The variables can be obtained by the following formula: $w=(X^TX)^{-1}X^Ty$. The implementation uses the formula to return the parameters $w_i$. As input, the implementation takes the variable matrix X and label matrix y to learn the model. "
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    "def multivarlinreg(X, y, quiet=False): \n",
    "    \"\"\"Function that implements linear regression with gradiant decent \n",
    "    x = data matrix\n",
    "    y = the dependent variable /the labels\n",
    "    \"\"\"\n",
    "    # When X is one dimensional, this will make the function run anyways\n",
    "    if len(X.shape) == 1: \n",
    "        X = X.reshape(-1,1)\n",
    "    \n",
    "    # instert a column of ones at index 0, for calculation of w0\n",
    "    w0_ones = np.ones((X.shape[0],))\n",
    "    X = np.insert(X, 0, w0_ones, axis=1)\n",
    "    \n",
    "    # Calculate wi\n",
    "    w = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "    \n",
    "    # Printing the reults if desireble \n",
    "    count = -1\n",
    "    if quiet == False:\n",
    "        for i in w: \n",
    "            count = count + 1\n",
    "            print('w' + str(count) + ': ' + str(i))\n",
    "            \n",
    "    return w"
   ]
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   "source": [
    "def pred(x_test, wi):\n",
    "    \"\"\"Function that predicts output values from the wi values\"\"\"\n",
    "    # instert a column of ones at index 0, for calculation of w0\n",
    "    w0_ones = np.ones((x_test.shape[0],))\n",
    "    x_test = np.insert(x_test, 0, w0_ones, axis=1)\n",
    "    \n",
    "    # make predictions\n",
    "    pred = np.dot(x_test, wi)\n",
    "    \n",
    "    return pred"
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    "def rmse(f, t): \n",
    "    \"\"\"Function that implements the root mean square error. \n",
    "    f = the predicted values of the dependent output variable\n",
    "    t = the ground truth values of dependent output variable\n",
    "    , an N-dimensional vector, as a numpy array\n",
    "    \"\"\"\n",
    "    f = np.array(f)\n",
    "    t = np.array(t)\n",
    "\n",
    "    diff = (f - t)**2\n",
    "    rmse = np.sqrt(np.mean(diff))\n",
    "    \n",
    "    print(\"Rmse: \" + str(rmse))\n",
    "    \n",
    "    return rmse"
   ]
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